Oblicz długości odcinków x,y,z.
1)
ctg30 = 6√3/ a
ctg(30+15) = 6√3/b
x = b-a
√3 = 6√3/a
a= 6√3/√3
a=6
ctg45= 6√3/b
1 = 6√3/b /*b
b= 6√3
x= 6- 6√3
2)
ctg45 = a/y
ctg(45+15) = a/b
b= 2+y
1 = a/y
y=a
ctg60 = y/b
√3/3 = y/b
y = b *√3/3
y= (2+y)√3/3
y= 2√3/3 + y√3/3
y- y√3/3= 2√3/3
y (1- √3/3) = 2√3/3 /:(1- √3/3)
y = 2√3/3-√3
y= 2/(√3-1)
3) ctg30 = z/a
ctg60 = z/b
a = b-4
√3=z/a
a = z/√3
b=z/√3/3
b= √3z
z/√3=√3z - 4
z/√3 - √3z = -4 /*√3
z - 3z = -4√3
-2z = -2√3 /: -2
z = √3
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1)
ctg30 = 6√3/ a
ctg(30+15) = 6√3/b
x = b-a
√3 = 6√3/a
a= 6√3/√3
a=6
ctg45= 6√3/b
1 = 6√3/b /*b
b= 6√3
x= 6- 6√3
2)
ctg45 = a/y
ctg(45+15) = a/b
b= 2+y
1 = a/y
y=a
ctg60 = y/b
√3/3 = y/b
y = b *√3/3
y= (2+y)√3/3
y= 2√3/3 + y√3/3
y- y√3/3= 2√3/3
y (1- √3/3) = 2√3/3 /:(1- √3/3)
y = 2√3/3-√3
y= 2/(√3-1)
3) ctg30 = z/a
ctg60 = z/b
a = b-4
√3=z/a
a = z/√3
b=z/√3/3
b= √3z
z/√3=√3z - 4
z/√3 - √3z = -4 /*√3
z - 3z = -4√3
-2z = -2√3 /: -2
z = √3